Dust particles effectively charged by plasma recently have been optically observed to exhibit crystalline phases not expected of Wigner or Yukawa crystals. Under varying conditions the crystal sometimes appears as deformed and oriented three-dimensional close-packed lattices of bcc, fcc, or hcp type, but mostly as a triangular array of vertical chains of particles. The unusual phases are shown to be caused by dipole-dipole interactions. The dipole moments are induced on the dust particles by gravity and by drag forces generated by ion stream. We describe in detail stable lattice structures and present the highly complex phase diagram of the dusty plasma. It turns out that in large parts of the phase diagram the stable phases indeed correspond to chains, but particles in neighboring chains belong to different sublattices. The stability of the lattices against excitations due to compression (i.e., aspect ratio variations) and vibration (i.e., phonons or charge density waves) is established.
